Intermediate Algebra II Sec. 6.1(Day1) Notes

Intermediate Algebra II Sec. 6.1(day1) notes

I.  Objective: To find nth roots.

Raising a number the nth power means using that number as a factor n times.

6n if n = 5 means 65

The opposite of raising a number to the nth power is taking the nth root.

Square Root – If a² = b, then a is a square root of b.

Ex1 Simplify
36
/ Ex1 Simplify
3125

nth Root – For any real numbers a and b and any positive integer n, if an= b, then a is an nth root of b.

·  Label the parts: nb

·  If n is odd, nbn = b

·  If n is even, nbn = b

·  If the index is even,

o  And b is positive; you must insure that the Principal Root is positive. (Go back to Ex1)…Therefore, you may have to use Absolute Value symbols if a variable is present.

o  and b is negative; there are no real nth roots of b.

·  The only nth root of 0 is 0.

Ex3 What are all the real square roots of
a)  25 / b)  49 / c)  -81
Ex4 What are all the real cube roots of
a)  0.008

/ b)  -1000 / c)  127
Ex5 What are all the real fourth roots of
a)  1

/ b)  -0.0001 / c)  1681

According to the Fundamental Theorem of Algebra, x4-1 has 4 roots, only 2 of which are real. In this chapter, the focus is on real roots only.

*If the index is even, you must insure that the Principal Root is positive.

Go back and find the Principal Roots for Ex3 & Ex5

Ex6 What is each real-number root?
a)  3-27 / b)  481 / c)  (-7)² / d)  -49

II.  Assignment: p384: 1-3all, 10-19all, 39,40